On Invariant Tori for a Stochastic Ito System

By using the Green function, we obtain conditions implying existence of invariant sets for Ito systems that are extensions of dynamical systems on a torus.     

Dmytro Ivanovych Martynyuk (On the 60th Anniversary of His Birth)

Ukrainian Mathematical Journal -     

Structure of Binary Transformations of Darboux Type and Their Application to Soliton Theory

On the basis of generalized Lagrange identity for pairs of formally adjoint multidimensional differential operators and a special differential geometric structure associated with this identity, we propose a general scheme of the construction of corresponding transformation operators that are described by nontrivial topological characteristics. We construct explicitly the corresponding integro-differential symbols of transformation operators, which are used in the construction of Lax-integrable nonlinear two-dimensional evolutionary equations and their Darboux–Bäcklund-type transformations.     

Solutions of systems of nonlinear difference-differential equations of neutral type asymptotically bounded in the entire axis

For a certain class of systems of difference-differential equations of neutral type, we study the properties of solutions asymptotically bounded on the entire axis.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 11, pp. 1597–1601, November, 1994.This work was supported by the Ukrainian State Committee on Science and Technology.